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Kushnir, Alexandra R.L. 2008. Understanding Multi-Peak Anomalies for Unexploded Ordnance Discrimination. Undergraduate Honours Thesis. Department of Earth and Ocean Sciences. University of British Columbia.
Kushnir, Alexandra R. L.
A workflow for the discrimination of multi-peak anomalies due to an unexploded ordnance (UXO) is presented. The effects of changes in the depth and orientation of a subsurface target on its TEM response are explored. Further, the variation of the peak separation, peak widths, maxima to minimum ratios and maxima values through time are modelled. Models of spatial and temporal variations are performed for both one and twotargets. These models are devoid of noise and focus primarily on the 3lb FLBGR bomb. It is found that the decay of the magnitudes of the anomaly maxima are related to the decay of the characteristic polarization curves of the UXO that creates them. The behaviour of the decay of the magnitudes of the maxima values of multi-peak anomalies is determined to be a good indication of target number in the subsurface. Observing these decays, it is possible to distinguish between two multi-peak scenarios, namely: a) a multipeak anomaly produced by a single UXO or two UXOs of the same type; and b) a multipeak anomaly produced by two UXOs of different types.
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Understanding Multi-Peak Anomalies for Unexploded Ordnance Discrimination by Alexandra Roma Larisa Kushnir A THESIS SUBMITED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELORS OF SCIENCE (HONOURS) in THE FACULTY OF SCIENCE Department of Earth and Ocean Sciences This thesis conforms to the required standard ……………………………….. Supervisor THE UNIVERSITY OF BRITISH COLUMBIA MARCH 2008 2 Abstract A workflow for the discrimination of multi-peak anomalies due to an unexploded ordnance (UXO) is presented. The effects of changes in the depth and orientation of a subsurface target on its TEM response are explored. Further, the variation of the peak separation, peak widths, maxima to minimum ratios and maxima values through time are modelled. Models of spatial and temporal variations are performed for both one and two- targets. These models are devoid of noise and focus primarily on the 3lb FLBGR bomb. It is found that the decay of the magnitudes of the anomaly maxima are related to the decay of the characteristic polarization curves of the UXO that creates them. The behaviour of the decay of the magnitudes of the maxima values of multi-peak anomalies is determined to be a good indication of target number in the subsurface. Observing these decays, it is possible to distinguish between two multi-peak scenarios, namely: a) a multi- peak anomaly produced by a single UXO or two UXOs of the same type; and b) a multi- peak anomaly produced by two UXOs of different types. 3 Table of Contents Abstract .......................................................................................................................... i Table of Figures............................................................................................................ iv Acknowledgments ........................................................................................................vi Chapter 1: Introduction................................................................................................ 1 1.1 Motivation............................................................................................................. 1 1.2 Goals and Assumptions ......................................................................................... 3 1.3 Thesis Outline ....................................................................................................... 4 Chapter 2: Time-domain Electromagnetics ................................................................. 5 2.1 Time-domain Electromagnetic Induction ............................................................... 5 2.2 The Geonics EM63................................................................................................ 7 2.3 Numerical Approximation Code and Datasets........................................................ 8 Chapter 3: Analytic Investigation ................................................................................ 9 3.1 An Analytic Approximation for Single Target Problems........................................ 9 3.2 Physical Interpretation of the Axial and Transverse Dipoles ................................ 14 3.3 Polarization Curves ............................................................................................. 16 3.4 Analytic Approximations for Three Different UXO Types................................... 18 3.5 Comparison Between Analytic and Numeric Approximations.............................. 22 3.6 Conclusion .......................................................................................................... 23 Chapter 4: Numeric Simulations – Spatial Variations .............................................. 24 4.1 Introduction......................................................................................................... 24 4.2 Simulation Setup and Measured Characteristics................................................... 24 4.3 The 3lb Bomb...................................................................................................... 26 4.4 TEM Response Variations with Changes in ! " ..................................................... 26 4.4.1 Expected Variations with ! " .......................................................................... 26 4.4.2 Numerically Modelled TEM Responses due to Changes in ! " ....................... 27 4.5 TEM Response Variation with Changes in Depth ................................................ 29 4.5.1 Expected Variations with Depth.................................................................... 29 4.5.2 Observed Variations with Depth ................................................................... 30 4.6 Conclusions......................................................................................................... 32 Chapter 5: Numeric Simulations: Temporal Variations ........................................... 34 5.1 Introduction......................................................................................................... 34 5.2 Synthetic Datasets ............................................................................................... 34 5.3 Comparison of Synthetic Datasets ....................................................................... 36 5.4 Further Modeling of Temporal Variations............................................................ 38 5.4.1 Peak Width ................................................................................................... 38 5.4.2 Maxima to Minimum Ratios ......................................................................... 39 5.4.3 Maxima Decay.............................................................................................. 40 5.5 Conclusion .......................................................................................................... 43 5.5.1 Peak Separation ............................................................................................ 43 5.5.2 Peak Width ................................................................................................... 44 5.5.3 Maxima to Minimum Ratios ......................................................................... 44 5.5.4 Decay of the Maxima Values ........................................................................ 45 4 Chapter 6: Synthetic Example: Two Targets of Different Types.............................. 47 6.1 Introduction......................................................................................................... 47 6.2 Synthetic Dataset................................................................................................. 47 6.3 ! L(t) Curves for the 3lb Bomb and ATC 105 mm................................................. 48 6.4 Maxima Decay .................................................................................................... 49 6.5 Conclusion .......................................................................................................... 50 Chapter 7: Conclusion ................................................................................................ 52 7.1 General Conclusions from Previous Chapters ...................................................... 52 7.2 A Workflow for Understanding Multi-peak Anomalies for UXO Discrimination. 54 7.3 Assumptions and Limitations............................................................................... 56 7.4 Future Work ........................................................................................................ 56 Appendix A: Polarization Constants.............................................................................. 58 Appendix B: Inversions of Synthetic Data..................................................................... 59 Bibliography ................................................................................................................. 70 5 Table of Figures Figure 1.1 - Some typical UXO (Pasion 2007)................................................................. 1 Figure 2.1 – Schematic drawing of time-domain electromagnetic techniques. ................. 5 Figure 2.2 – A TEM detection system: the Geonics EM63. .............................................. 7 Figure 3.1 – Survey configuration and the relationship between the global and body-fixed coordinate systems. ................................................................................................. 9 Figure 3.2 – The TEM response due to a horizontal (a) and vertical (b) UXO target when ! L 1 (t) > L 2 (t) . ......................................................................................................... 15 Figure 3.3 – The normalized ! ˆ z components of ! r " total , r " axial and r " transverse .......................... 17 Figure 3.4 – The analytic approximation for ! 1" L 1 (t) L 2 (t) "10 . The red curves show the total TEM response. The blue and green curves show the response due the axial and transverse components of the induced dipole, respectively. Note that a two-peak anomaly occurs when ! L 1 (t) L 2 (t) " 3............................................................................. 18 Figure 3.5 - ! L 1 (t) L 2 (t) for three UXO types: the 3lb bomb (blue), the ATC 105 mm (green) and the ATC MK 118 (red). The pink line represents ! L 1 (t) L 2 (t) = 3............................. 19 Figure 3.6 – Analytically (red) and numerically (blue) modelled responses for the 3lb bomb at time channels 1, 13, 14, and 26. ............................................................... 20 Figure 3.7 – Analytically (red) and numerically (blue) modelled responses for the ATC 105 mm at time channels 1, 13, 14, and 26. ........................................................... 21 Figure 3.8 – Analytically (red) and numerically (blue) modelled responses for the ATC MK 118 at time channels 1, 13, 14, and 26. ........................................................... 21 Figure 4.1 – Schematic of a two-peak anomaly detailing the measured features used throughout the rest of this paper. ........................................................................... 25 Figure 4.2 – ! L 1 (t) (red) and ! L 2 (t) (blue) for the 3lb bomb. ........................................... 26 Figure 4.3 – The normalized TEM response of the 3lb bomb as ! " varies from ! 0° to ! 90°. .............................................................................................................................. 27 Figure 4.4 – Peak separation as a function of ! " . The red line is a line of best fit... ....... 28 Figure 4.5 – Peak width as a function of ! " . The red dots represent the peak width of a single peak anomaly when one peak is observed. The blue and green represent the peak widths of peak 1 and peak 2, respectively, when two peaks are observed. ...... 29 Figure 4.6 – The normalized TEM responses at time channel 1 for varying UXO burial depths.................................................................................................................... 30 Figure 4.7 – Peak separation as a function of depth for a horizontal 3lb bomb.............. 31 Figure 4.8 – Peak width as a function of depth for a horizontal 3lb bomb. .................... 32 Figure 5.1 – Synthetic datasets at time channel 1: a two-peak anomaly produced by a single UXO (top left) and a two-peak anomaly produced by two UXO (top right). Both datasets are normalized to their respective maxima values. The absolute (bottom left) and relative differences (bottom right) are also shown....................... 35 6 Figure 5.2 – Peak separation, peak width, maxima values and maxima to minimum ratios through time for the single target dataset............................................................... 36 Figure 5.3 – Peak separation, peak width, maxima values and maxima to minimum ratios through time for the two target dataset. ................................................................. 37 Figure 5.4 – Peak width for the two-target scenario for varying ! " through time. The solid lines are the peak widths of peak 1 and the dashed lines are the peak widths of peak 2.................................................................................................................... 39 Figure 5.5 – Maxima to minimum ratios for peak 1 (5.5a, left) and peak 2 (5.5b, right). 40 Figure 5.6 – The normalized decays of the maxima values through time for the single- target (left) and two-target (right) scenarios.......................................................... 41 Figure 5.7 – The decays of the maxima values through time for the single-target scenario. The decays of ! m 1 (left) and ! m 2 (right) are observed for varying burial depths....... 42 Figure 5.8 – The decays of the maxima values through time for the single-target scenario. The decays of ! m 1 (left) and ! m 2 (right) are observed for varying ! " .. ...................... 42 Figure 5.9 – The decays of the maxima values through time for the two-target scenario. The decays of ! m 1 (left) and ! m 2 (right) are observed for varying ! " .. ...................... 43 Figure 6.1 – The test dataset: plan view (left) and line profile (right) taken across the anomaly peaks, for y = 0.0 m................................................................................. 48 Figure 6.2 – The ! L 1 (t) (red) and ! L 2 (t) (blue) curves for the 3lb bomb (solid lines) and the ATC 105 mm (dashed lines). ............................................................................ 49 Figure 6.3 – The non-normalized (6.3a, left) and normalized (6.3b, right) polarization curves and decays of ! m 1 and ! m 2 for the test scenario. ........................................... 50 Figure 7.1 – Workflow for discriminating between multi-peak anomalies produced by one and two targets in the subsurface........................................................................... 55 Figure B1 – Inversion of a synthetic dataset (see Section 5.2) where one 3lb bomb is oriented such that ! " = 90° and d = 0.2 m. The inversion is successful................... 67 Figure B2 – Inversion of a synthetic dataset where two 3lb bomb are oriented such that ! " = 0° and d = 0.2 m. The objects are placed 0.8 m apart. The inversion is unsuccessful. ......................................................................................................... 68 Figure B3 – Inversion of a synthetic dataset where a 3lb bomb at x = 0.4 m with ! " =10° and an ATC 105 mm at x = -0.4 m with ! " = 70° are modelled. The inversion is unsuccessful. ......................................................................................................... 69 7 Acknowledgments First and foremost, I would like to extend my sincerest thanks to Leonard Pasion for always being willing to discuss my thesis and helping me through snags along the way. His help has been enormous and without it this thesis would not have been possible. To Dave Sinex, I would also like to extend my gratitude. The infinite exchange of emails regarding the numerous problems I encountered while writing the code necessary to complete this thesis was invaluable. Thank you to Doug Oldenburg for giving me the opportunity to work on this project, but most importantly for teaching me that all I have to do is sit down, breath, and think, the rest is sure to come. To my parents who have been witness to my seventeen years of education: I’m impressed we’re all still sane. Thank you for your support and the encouragement to pursue what I love, whatever it may be. To the most unofficial club on campus: the Geophysics Group – all four of you. You have made this program the most memorable and enjoyable experience I could have hoped for. A little beer always helps too. And finally, to those people who stared me in the eye everyday and without a glimmer of doubt in their eye told me that I would finish this. That unwavering confidence has been the most precious gift I have ever received. 8 Chapter 1: Introduction 1.1 Motivation Unexploded ordnances (UXOs) are munitions which have been launched or fired but have failed to detonate on contact with their target (Beran 2005; Pasion et. al. 2001; Pasion 2007). They may remain at the surface of the earth or be buried up to 8 m into the subsurface (Pasion 2007). These munitions pose significant risk in current and post- conflict areas. In the United States alone, UXO remediation is estimated to cost $52 billion with the Department of Defense spending $200 million per year on clean-up (Pasion 2007). Military training in the United States is responsible for 10 million acres of land contaminated by UXOs and it is estimated that 10,000 new UXOs are created every year (Beran 2005). Approximately 70% of the cost associated with UXO remediation is spent on excavation of non-ordnance items (Beran 2005), therefore efficient detection techniques are needed to reduce the cost of remediation by eliminating unnecessary excavation. Figure 1.1 - Some typical UXO (Pasion 2007). 9 UXO detection involves determining the location of subsurface targets. The traditional procedure for identifying possible UXO targets is called “mag and flag” (Pasion 2007; Beran 2005). This approach - in which a metal detector is used to flag a metallic object in the subsurface for excavation - is both inefficient and subjective, leading to false alarm rates of up to 100 metallic non-UXO detections for every one UXO (Beran 2005). These false positives may result from shrapnel, geology, or range scrap. A variety of geophysical sensing techniques are available for UXO detection. Magnetic investigations, such as metal detectors, are plagued by the inherent non- uniqueness associated with determining the orientation, size, and shape of a target (Billings 2004). Magnetic techniques are also extremely susceptible to geological noise (Pasion 2007). Electromagnetic induction (EMI) techniques, in contrast, are attractive for UXO detection as they are relatively immune to geological noise and provide diagnostic parameters for the shape, size and orientation of the target (Pasion 2007). They are limited, however, by their reduced depth of investigation (Pasion 2007). Time-domain electromagnetic (TEM) techniques involve illuminating the Earth’s subsurface using a time varying magnetic field which induces currents on the surface of metallic objects in the subsurface (Pasion et. al. 2001). These surface currents generate a secondary magnetic field, which is detected at the surface of the Earth. Once this primary field is terminated, the induced currents diffuse inward, resulting in the decay of the secondary magnetic field through time (Pasion et. al. 2001). The rate of decay of this secondary field provides information of the target’s material properties, shape and orientation (Pasion et al. 2001). Pasion et. al. (2001) presented an approximate model for 10 the TEM response of a metallic object. This two-dipole model models the TEM response of a UXO as a pair of perpendicular dipoles located at the centre of the metallic object. The shape of the target UXO and the configuration of the detection system determines the spatial shape of the secondary signal. A single, isolated, rod-like target can produce a TEM anomaly with either a single, or a pair of peaks (Pasion 2007). Multi-peak signals pose significant problems for data processing methods. In particular, a decision must be made whether to invert the multi-peak anomaly as a single target, or a pair of targets. In order to begin to develop a methodology for discriminating between two-peak anomalies generated by one and two targets, it is important to understand under what survey conditions two-peak anomalies occur. The shape and material properties of the UXO target also play an important role in determining the spatial shape of the TEM response for particular ordnance types. An understanding of how these two-peak responses vary spatially and temporally must be established. 1.2 Goals and Assumptions The goal of this thesis is to establish a workflow capable to discriminating between three key scenarios: 1. A two-peak anomaly due to a single UXO target 2. A two-peak anomaly due to two UXO targets of the same type 3. A two-peak anomaly due to two UXO targets of different types Before proceeding, it is prudent to outline the assumptions made in this paper. It is assumed that the types of UXOs contaminating a given site under investigation are 11 known and that the depth of burial and orientation of any UXOs in the subsurface are not known. The scope of this paper is restricted to analysis of two peak anomalies and the datasets created are densely sampled and contain no noise. 1.3 Thesis Outline I begin by developing a dipole-based analytic approximation for the multi-peak problem and comparing this approximation with numerical models. Using these numerical models, I examine the spatial and temporal characteristics of the TEM responses. These models are performed using a 3lb bomb, which was used during training exercises at the Former Lowry Bombing and Gunnery Range (FLBGR). I expand these forward models to scenarios in which one and two 3lb bombs produce two- peak anomalies. Finally, I develop a workflow, which uses the results of these investigations to help discriminate between individual targets prior to inversion of a TEM dataset. 12 Chapter 2: Time-domain Electromagnetics 2.1 Time-domain Electromagnetic Induction Inductive time-domain electromagnetic (TEM) methods employ a source through which a current is run then switched off (Oldenburg 2007). TEM surveys may be airplane mounted, allowing for large amounts of data to be acquired at a relatively low cost, but for UXO detection purposes, ground surveys are needed to acquire adequate spatial resolution of individual targets. Transmitter Loop Receiver Loop Su rfa ce C urr en ts Surface P rim ary F ield S ec on da ry F ie ld Conductive Target Non-conducting subsurface Primary Field a r Figure 2.1 – Schematic drawing of time-domain electromagnetic techniques. The transmitter is a loop of wire connected to a current source, which is subsequently turned off. The current running through the loop of the transmitter produces a magnetic field. This is called the primary magnetic field ( ! r H p). Strictly speaking, the direction of the primary field is dependent on the orientation of the wire, 13 but if the target is far enough away from the transmitter ( ! r >> a , where r is the distance between the target and the transmitter and a is the radius of the circular transmitter loop), the source can be approximated by a magnetic dipole (Oldenburg 2007). It is assumed that the subsurface is resistive to ensure that the primary field is not altered as it penetrates the ground (Griffiths 1999). The success of TEM techniques in UXO detection is due to the large contrast in conductivity between the ground and the buried metallic target. Consequently, we assume that the target of interest sits in free space. When the current running though the transmitter loop is turned off, there will be a change in magnetic flux, ! d r B p dt , at the target. By Faraday’s law, the change in magnetic flux induces an electrical force in conductive objects in the subsurface: ! r " # r E = $% r B p %t (Equation 1) where ! r E is the electric field (Griffiths 1999). This electrical force induces a current whose strength is governed by Ohm’s law: ! r J =" r E (Equation 2) where ! r J is the current density and ! " is the electrical conductivity of the target. Following from Ampere’s law, this induced current density gives rise to a magnetic field. This induced magnetic field is called the secondary magnetic field ( ! r H s ). Since ! r E varies with time in the target, ! r H s also varies with time. At the receiver loop, the measured voltage is due to the rate of change of the secondary magnetic flux, ! d r B s dt , and is given by: 14 ! V = "N dF dt (Equation 3) where V is the measured voltage, and ! F = r B " ˆ nd r a # is the integral of the component of the magnetic flux perpendicular to the receiver loop (Oldenburg 2007). From calibration information specific to the TEM system used, the secondary magnetic flux may be calculated. 2.2 The Geonics EM63 A typical TEM system is shown in Figure 2.2. The Geonics EM63 consists of a horizontal, ! 1 m "1 m transmitter loop located a distance, h, above the ground surface (Geonics 2008). The system produces a pulsed primary magnetic field, which induces eddy currents in subsurface targets (Geonics 2008). The decay of the induced eddy currents give rise to a secondary magnetic field whose decay rate is determined by the orientation, size, shape, and material properties of the target (Geonics 2008). The secondary magnetic field is recorded at 26 time channels ranging from ! 180 µs to ! 25 ms . Figure 2.2 – A TEM detection system: the Geonics EM63. 15 2.3 Numerical Approximation Code and Datasets In this paper, numeric modelling is performed using a forward modelling code in UXOLab, a product of the University of British Columbia. The code is used to create synthetic datasets, taking into account the finite geometry of the Geonics EM63. For the purposes of this paper, the transmitter loop is located h = 0.3 m above the surface of the Earth and its size is kept to specification (1 m x 1 m). The code is capable of modelling both single and two target scenarios but does not include noise. 16 Chapter 3: Analytic Investigation 3.1 An Analytic Approximation for Single Target Problems In deriving an analytic approximation, all UXOs and the majority of buried metallic scrap may be adequately described as axi-symmetric (Pasion et. al. 2001). Figure 3.1 shows the survey configuration assumed throughout the rest of this thesis. In this configuration, the transmitter and receiver loops are located at the same location, their centers defined by ! r r t = xt yt zt[ ], in Cartesian coordinates. The length of one side of the square transmitter loop is denoted ! a . The UXO target is located in the subsurface at position ! r r o = [xo yo zo ]. Transmitter Loop Surface r-R R r UXO z y x x' y ' _ z' _ h d z y x x' y' z ' Figure 3.1 – Survey configuration and the relationship between the global (black) and body-fixed (red) coordinate systems. 17 Two different coordinate systems are used to solve this problem (Pasion et. al. 2001). One is a global coordinate system, which remains fixed in space. It is in this coordinate system that the transmitter and receiver loops are defined. The second coordinate system is fixed to the UXO target and may rotate with the target through space. This is called the body fixed coordinate system. It is defined such that the ! ˆ z' axis is always aligned with the long axis of the UXO. Assuming, an axially symmetric UXO, there is symmetry about the ! ˆ z' direction. ! " is the angle between ! ˆ z' and ! ˆ z and ! " is the angle between the projection of ! ˆ z' onto the horizontal plane and ! ˆ x (Pasion 2007). In this paper, ! " remains 0 for all simulations. This is done as ! " only serves to rotate the TEM response in the x-y plane, therefore, aside from changing the location of the anomalies, it plays no role in changing the morphology of the TEM response. A line profile taken along the surface of a topography-free earth in the ! ˆ x-direction is considered. The line profile is taken over the UXO target. Both ! yo and ! yt are 0 while ! x o , ! z o and ! z t remain constant. The distance between the UXO target and the centre of the transmitter loop is defined: ! r = (xo " xt ) 2 + (zo " zt ) 2 (Equation 4) If ! r >> a , we may approximate the source loop by a magnetic dipole located at ! r r . Using this approximation, the magnetic flux due to a magnetic dipole source, ! r m p , at a distance r from the source is given: ! r B p = µo 4"r3 3( r m p # ˆ r )ˆ r $ r m p( ) (Equation 5) 18 where ! µ o = 4" #10$7 N /A2 is the permeability of free space and ! r B p is the primary magnetic flux at a distance r from the source. ! r m p and ! ˆ r are defined: ! r m p = mx my mz [ ] (Equation 6) ˆ r = r r o " r r t r (Equation 7) If the transmitter loop is horizontal (as in the case of the EM63), it can be approximated by a single vertical magnetic dipole oriented in the ! ˆ z direction. ! r m p becomes: ! r m p = 0 0 mz[ ] (Equation 8) Substituting r and ! r m p into Equation 5, ! r B p becomes: ! r B p = Bx p By p Bz p[ ] (Equation 9a) where ! Bx p , ! By p , and ! Bz p are the x, y, and z components of the primary magnetic flux at the UXO target: 19 ! Bx p = µo 4"r3 3mz(zo # z)(xo # x) r 2 $ % & ' ( ) (Equation 9b) By p = µo 4"r3 3mz(zo # z)(yo # y) r 2 $ % & ' ( ) (Equation 9c) Bz p = µo 4"r3 3mz(zo # z) 2 r 2 #mz $ % & ' ( ) (Equation 9d) Switching from the body centered coordinate system to the global coordinate system, the rotation matrix A is defined: ! A = ˆ x ' ˆ y ' ˆ z ' " # $ $ $ % & ' ' ' = sin( 0 cos( 0 )1 0 cos( 0 )sin( " # $ $ $ % & ' ' ' ˆ x ˆ y ˆ z " # $ $ $ % & ' ' ' (Equation 10) When ! " = 0°, ! ˆ z' is perpendicular to ! ˆ x and when ! " = 90°, ! ˆ z' is parallel to ! ˆ x . If the UXO target is axially symmetric, the induced magnetic dipole due to ! r B p can be described by the linear combination of two orthogonal dipoles located at the centre of the UXO target (Beran 2005; Pasion 2001; Pasion 2007). These dipoles are called the axial and the transverse dipoles. The axial dipole lies along the ! ˆ z' direction, therefore, ! r m axial = (ˆ z '" r B p )ˆ z ' (Equation 11) Similarly, the transverse dipole is the sum of the ! ˆ x' and ! ˆ y' components of the induced magnetic dipole: ! r m transverse = ( ˆ x '" r B p ) ˆ x '+( ˆ y '" r B p ) ˆ y '( ) (Equation 12) 20 The axial and transverse components of the secondary magnetic field at the receiver are found by substituting ! r m axial and ! r m transverse for ! r m p into Equation 5: ! r " axial = A µo 4#r3 3( r m axial $ ˆ r ) ˆ r % r m axial( ) & ' ( ) * + (Equation 13a) r " transverse = A µo 4#r3 3( r m transverse $ ˆ r ) ˆ r % r m transverse( ) & ' ( ) * + (Equation 13b) The relative strengths of the induced secondary magnetic fluxes due to the axial and transverse dipoles are determined by the shape and material properties of the UXO target. These properties are encompassed by ! L(t) = L 3 (t) 0 0 0 L 2 (t) 0 0 0 L 1 (t) " # $ $ $ % & ' ' ' , where ! L 1 (t) , ! L 2 (t) and ! L 3 (t) are the time varying polarizations of the UXO target in the ! ˆ x', ! ˆ y' and ! ˆ z' directions, respectively. These values are defined: ! Li(t) = kit "# i e "t $ i (Equation 14) where i is either 1, 2, or 3 and ! k i controls the magnitude of the modelled responses. ! " i and ! " i define the decay of different parts of the polarization curve. The polarization curve is divided into two parts: an intermediate time part and a late time part. The decay of the intermediate time part of the curve is governed by ! " i , while that of the late time part is controlled by ! " i (there exists an early time part to the polarization curve, but most TEM systems do not record this part, therefore it is ignored here). For an axially symmetric UXO, ! L 2 (t) and ! L 3 (t) are equal and for rod-like targets, ! L 1 (t) is larger than ! L 2 (t) . 21 In practice, the receiver is a horizontal loop, therefore only the components of ! r " axial and ! r " transverse in the ẑ -direction intersect the loop and give rise to an induced voltage. Combining all the above information, the total secondary magnetic flux at the receiver is defined by the linear combination of the z-components of ! r " axial and ! r " transverse scaled by ! L(t): ! r B z S = r B transverse S + r B transverse S (Equation 15) where: ! r B axial S = L1(t)(ˆ z " r # axial )ˆ z (Equation 16a) r B transverse S = L2(t)(ˆ z " r # transverse )ˆ z (Equation 16b) 3.2 Physical Interpretation of the Axial and Transverse Dipoles Figure 3.2a considers a UXO oriented such that ! " = 90°. It is assumed that ! L 1 (t) > L 2 (t) . The red and blue arrows represent the relative strengths of the axial and transverse dipoles, respectively. A horizontal transmitter loop is moved over the UXO in the x̂ -direction. At x = A, the field lines of the primary magnetic field impinge upon the UXO parallel to the 'ẑ -direction, preferentially exciting a dipole in the axial direction. The induced axial dipole gives rise to a secondary magnetic field whose field lines are perpendicular to the plane of the transmitter loop, inducing a current in the receiver loop. As x approaches B, the primary magnetic field lines begin to impinge upon the UXO more obliquely until x = B, when the field lines impinge the UXO perpendicular to the 22 'ẑ -direction. The magnitude of the induced transverse dipole is small, resulting in a local minimum in the TEM response. At x = C, by symmetry and recalling the TEM response when x = A, a local maximum is induced by a preferentially excited dipole in the axial direction. x=A x=B x=C x=A x=B x=C a) b) Figure 3.2 – The TEM response due to a horizontal (a) and vertical (b) UXO target when ! L 1 (t) > L 2 (t) . 23 Similarly, Figure 3.2b considers the same UXO oriented at ! " = 0°. At x = A, the primary field lines impinge upon the UXO parallel to 'x̂ , exciting a dipole in the transverse direction, inducing a relatively small secondary field at the receiver loop. When x = B, the axial dipole is preferentially excited, producing a local maximum. Again, by symmetry, when x = C, the TEM response decreases, ensuring that the final total secondary field is dominated by a single peak. Figure 3.2 presents the end member cases for variations in ! " . The transition between ! " = 90° and ! " = 0° is expected to be a continuum, with a symmetrical double peak progressively forming as ! " approaches ! 90°. 3.3 Polarization Curves Plotting ! (ˆ z " r # axial )ˆ z , ! (ˆ z " r # transverse ) ˆ z , and ! " total = ( ˆ z # r " axial ) ˆ z + (ˆ z # r " transverse )ˆ z for ! " = 90° and ! x t between -2.0 m and 2.0 m, Figure 3.3 is produced. From Figure 3.2, it is evident that the induced axial dipole is responsible for the double peak component of any total secondary magnetic field curve. Since the axial and transverse dipoles may be added linearly to give the total magnetic field, the occurrence of a double peak for any given UXO is controlled by the ratio ! L 1 (t) L 2 (t) . It is clear that when ! L 1 (t) L 2 (t) =1, the transverse dipole dominates the total secondary magnetic field, ensuring that it is represented by a single peak. 24 Figure 3.3 – The normalized ! ˆ z components of ! r " total , r " axial and r " transverse . It is reasonable to assume that there should be a threshold ! L 1 (t) L 2 (t) ratio above which a double peak would be expected to be produced. This is explored analytically using Equations 16a and 16b. Figure 3.4 shows ! r B axial s and ! r B transverse s (calculated at the receiver loop) for ! L 1 (t) L 2 (t) ratios ranging from 1 to 10. The axial component of the induced dipole begins to dominate the total signal when ! L 1 (t) L 2 (t) " 3. 25 Figure 3.4 – The analytic approximation for ! 1" L 1 (t) L 2 (t) "10 . The red curves show the total TEM response. The blue and green curves show the response due the axial and transverse components of the induced dipole, respectively. Note that a two-peak anomaly occurs when ! L 1 (t) L 2 (t) " 3. 3.4 Analytic Approximations for Three Different UXO Types In Section 3.3, it was determined that when ! L 1 (t) L 2 (t) " 3, a two-peak anomaly begins to dominate the total secondary magnetic field. To evaluate the validity of this conclusion, three different ordnance types are examined: a) the 3lb FLBGR bomb, b) the ATC 105 mm, and c) the ATC MK 118. All three UXOs are oriented such that ! " = 90° to ensure that their orientations are most conducive to producing multiple peak anomalies and the ratio ! L 1 (t) L 2 (t) of their polarization curves are plotted in Figure 3.5. The pink line 26 indicates ! L 1 (t) L 2 (t) = 3 therefore, all points above this line represent time channels for which double peak anomalies are theoretically expected. Figure 3.5 - ! L 1 (t) L 2 (t) for three UXO types: the 3lb bomb (blue), the ATC 105 mm (green) and the ATC MK 118 (red). The pink line represents ! L 1 (t) L 2 (t) = 3 ! L 1 (t) L 2 (t) is greater than 3 at all time channels for the 3lb bomb. The same ratio is greater than 3 at all time channels after time channel 13 for the ATC 105 mm. ! L 1 (t) L 2 (t) is never greater than 3 for the ATC MK 118. From these observations, it is expected that the 3lb bomb will produce a multi-peak anomaly for all time channels, while the ATC 105 mm will only produce multi-peak anomalies for time channels after 13. The ATC MK 118 is never expected to produce a multi-peak anomaly. 27 Figures 3.6 to 3.8 show the secondary magnetic field responses due to the three different UXO types at time channels 1, 13, 14, and 26. The red curves show analytically derived responses. As expected, the 3lb bomb (Figure 3.6) produces a double peak for all time channels and the ATC MK 118 (Figure 3.8) never produces a double peak. A double peak is observed for the ATC 105 mm (Figure 3.7) after time channel 13. Figure 3.6 – Analytically (red) and numerically (blue) modelled responses for the 3lb bomb at time channels 1, 13, 14, and 26. 28 Figure 3.7 – Analytically (red) and numerically (blue) modelled responses for the ATC 105 mm at time channels 1, 13, 14, and 26. Figure 3.8 – Analytically (red) and numerically (blue) modelled responses for the ATC MK 118 at time channels 1, 13, 14, and 26. 29 3.5 Comparison between Analytic and Numeric Approximations The analytic approximation presented in Section 3.1 solves the single target UXO problem using perfect dipoles. In reality, however, the apparatus used for detection can only be approximated by perfect dipoles, and thus the analytic approximation is not expected to adhere completely to the observed data. To show this, the analytic simulations performed in Section 3.4, are repeated using numeric simulations of the Geonics EM63. The blue curves in Figures 3.6 to 3.8 show the numeric analogues to the analytic approximations discussed above. Both solutions are scaled to the maximum values of the numeric solution. This is done because the analytic approximation is orders of magnitude smaller than the numeric solution. This disparity in magnitude arises because the EM63 is an electronic system and measures a voltage induced by the secondary magnetic field in the receiver. The analytic approximation is solved directly for the secondary field. Both approximations, however, should reflect the shape of the TEM response accurately and it is on this basis that the two are compared. Comparing both solutions, we see that the signals are not identical. The widths of all anomaly peaks are greater in the case of the numeric solution. For all cases where double peaks are observed, the peak separation of the numeric solution is visibly greater than that of the analytic approximation. 3.6 Conclusion In this chapter I presented an analytic approximation of the TEM response of a single target. As shown in Figure 3.3, the transverse dipole dominates the TEM response 30 when ! L 1 (t) L 2 (t) =1, therefore, ! L 1 (t) must exceed ! L 2 (t) by some factor in order to dominate the signal. This approximation is used to determine that when ! L 1 (t) L 2 (t) " 3, a UXO is capable of producing a two-peak anomaly. This statement is tested by modelling the responses of the three UXOs: the 3lb bomb, the ATC 105 mm and the ATC MK 118. The hypothesis is found to be consistent. Comparing the analytic approximation and numeric solution, the differences in the peak widths and separations of the anomalies is due to the finite geometry of the transmitter loop used in the numeric solution. The shapes of the primary magnetic field due to a perfect dipole and square loop are different. The primary magnetic field due to a square loop may only be approximated by a perfect dipole if the observer is sufficiently far away from the loop. 31 Chapter 4: Numeric Simulations – Spatial Variations 4.1 Introduction Further analysis of the two-peak UXO problem is conducted using the numerical code introduced in Section 2.3. The 3lb FLBGR bomb is modelled since it is observed to produce a multi-peak anomaly at all time channels when ! " = 90°. The modelled response of the 3lb bomb is expected not only to vary temporally as the signal decays through time, but also spatially as ! " and d change. In this chapter the effects on the TEM response of changing the orientation of the UXO target is explored. All observations are made at the first time channel. 4.2 Simulation Setup and Measured Characteristics Before proceeding to an examination of synthetic datasets, it is useful to define the variables mentioned throughout the rest of this paper. Figure 4.1 is a schematic representation of a two-peak anomaly. 32 w2,1 w2,2 s m1 m2 w1 Peak 1 Peak 2 Figure 4.1 – Schematic of a two-peak anomaly detailing the measured features used throughout the rest of this paper. The two peaks are denoted peak 1 and peak 2 and their respective maxima values are denoted ! m 1 and ! m 2 . ! s is the value of the local minimum (or saddle point) between two peaks. The peak separation between the two maxima is denoted ! w 1 . Peak widths ( ! w 2 ) are defined by the full width at half maximum of the peaks. For the two-peak scenario, the half maximum is measured between the local minimum (s) and ! m 1 and ! m 2 . The peak width of peak 1 and peak 2 are denoted ! w 2,1 and ! w 2,2 , respectively. The ratios between the maxima values and the saddle point value are given by ! m i s , where i is the peak number. All measurements are made using a line profile taken across the maxima values of the synthetic datasets. These datasets are of good quality and contain no noise. 33 4.3 The 3lb Bomb Figure 4.2 is a plot of the polarization curves, ! L 1 (t) and ! L 2 (t) , for the 3lb bomb. It is clear that ! L 1 (t) is particularly strong. Indeed in Section 3.4, ! L 1 (t) was found to always be greater than ! L 2 (t) by a factor of 3. This characteristic makes the 3lb bomb a unique ordnance, and it should be noted that this exceptionally large ! L 1 (t) is not diagnostic of most ordnance types. The analysis conducted on the 3lb bomb below, however, may be applied to all types of UXO, therefore the work presented is not in vain. Figure 4.2 – ! L 1 (t) (red) and ! L 2 (t) (blue) for the 3lb bomb. 4.4 TEM Response Variations with Changes in ! " 4.4.1 Expected Variations with ! " As shown in Figure 3.6, a 3lb bomb oriented at ! " = 90° produces a symmetrical two-peak response when surveyed using a horizontal transmitter loop. From discussions 34 in Section 3.2, it is expected that when varying ! " between ! 0° and ! 90°, the two-peak responses will be more prominent for greater ! " . 4.4.2 Numerically Modelled TEM Responses due to Changes in ! " A synthetic dataset is created by modelling a single 3lb bomb with a depth of burial of d = 0.2 m and a transmitter loop height of h = 0.3 m. ! " is progressively varied from ! 0° to ! 90° at ! 5° increments. The dataset is sampled at 0.10 m. Figure 4.3 shows the responses of the secondary magnetic field for the first time channel when ! " = 0°,45°,75°, and 90° . These responses are normalized to the maximum response for all ! " so that their relative strengths may be assessed. Figure 4.3 – The normalized TEM response of the 3lb bomb as ! " varies from ! 0° to ! 90°. As expected, a two-peak anomaly becomes progressively more prominent as ! " approaches ! 90°. At ! " # 30°, the axial dipole is excited strongly enough to begin to dominate the total field signal and introduce a double peak. The relative strengths of the 35 responses decreases with increasing ! " . The peak separations ( ! w 1 ) for ! " # 30° are plotted in Figure 4.4. The slope of the line of best fit is ! "0.002 , indicating that there is only a small decrease in ! w 1 as ! " increases. Figure 4.4 – Peak separation as a function of ! " . The red line is a line of best fit. Figure 4.5 is a plot of peak width as a function of ! " . Three different ! w 2 are plotted: ! w 2 for ! 0° "# < 30°, when only one peak is observed and ! w 2,1 and ! w 2,2 when two peaks are observed ( ! 30° "# " 90°). At ! " = 90°, both ! w 2,1 and ! w 2,2 are equal, reflecting the symmetry of the TEM response. For ! " < 90°, ! w 2,1 is greater than ! w 2,2 and remains relatively constant. There is more scatter in ! w 2,2 which may be attributed to numerical noise as the sampling interval is 0.10 m. 36 Figure 4.5 – Peak width as a function of ! " . The red dots represent the peak width of a single peak anomaly when one peak is observed. The blue and green represent the peak widths of peak 1 and peak 2, respectively, when two peaks are observed. 4.5 TEM Response Variation with Changes in Depth 4.5.1 Expected Variations with Depth Magnetic field flux decreases as ! 1 r 3 , therefore the secondary magnetic flux measured at the receiver loop due to the induced magnetic dipole at the target decreases as ! 1 r 6 . As the distance between the transmitter loop and potential UXO target is increased, the amplitude of the secondary magnetic field decreases. With increasing depth, the amplitude of the TEM response is expected to decrease – the more deeply buried the target, the weaker its TEM response will become. 37 4.5.2 Observed Variations with Depth To observe the effect of changing the depth of burial of a UXO on the nature of the TEM response, a 3lb bomb oriented at ! " = 90° is modelled with h = 0.3 m, and a sample interval of 0.05 m. The depth, d, of the UXO is varied from ! 0.0 m to ! 1.6 m , at 0.2 m intervals. Figure 4.6 shows line profiles of the TEM response for y = 0.0 m for all d for time channel 1. The datasets are normalized to the maximum values of the strongest response (ie. the maximum value of the dataset when d = 0.0 m). The magnitude of the signal decreases with increasing depth, as expected. Figure 4.6 – The normalized TEM responses at time channel 1 for varying UXO burial depths. Peak separation is plotted as a function of d for the first time channel in Figure 4.7. With increasing d, the peak separation of a double peak anomaly increases linearly. Fitting this relation to a line using a least squares fit (Gubbins 2004), returns a relationship between peak separation and depth: ! w 1 = 0.65d + 0.59 . 38 Figure 4.7 – Peak separation as a function of depth for a horizontal 3lb bomb. Figure 4.8 is a plot of peak width as a function of depth at time channel 1. As observed in Section 4.4.2, the peak widths ( ! w 2 ) for a UXO with ! " = 90° are equal since the response is symmetrical, therefore, only one peak is plotted in Figure 4.8. Like ! w 1 , ! w 2 increases linearly with depth. Fitting the data with a line gives the relation: ! w 2 = 0.69d + 0.30. 39 Figure 4.8 – Peak width as a function of depth for a horizontal 3lb bomb. 4.6 Conclusions In Section 4.4.2, it was found that the development of a multi-peak anomaly is strongly dependent on ! " . In the case of the 3lb bomb, a multi-peak anomaly is produced for ! " # 30°. Consequently, not only does the ratio of ! L 1 (t) to ! L 2 (t) determine if a double peak is possible, but ! " must also be large enough to allow the primary field lines to couple with the axial dipole from a distance, as opposed to from directly above the target. The magnitude of the TEM response decreases as ! " increases. For the primary field to couple with the axial dipole when ! " # 30°, the transmitter loop must be relatively far away from the target. Since the TEM response decreases as ! 1 r 6 , the magnitude of the signal will decrease as ! " increases. 40 Peak separation and peak width do not appear to change significantly with changing ! " . ! w 1 is found to remain almost constant as the UXO is rotated. ! w 2,1 also appears to remain almost constant, decreasing when ! " = 90° so that ! w 2,1 equals ! w 2,2 . In general, however, neither ! w 1 nor ! w 2 appear to change with ! " . Both ! w 1 and ! w 2 increase linearly as the depth of burial of the 3lb bomb increases. These linear relationships are found in Section 4.5.2 and may be used as general rules for how ! w 1 and ! w 2 change with depth for the 3lb bomb. Before concluding that ! w 1 and ! w 2 increase linearly with depth for all UXO, the simulations performed in Section 4.5.2 must be repeated for at least a subset of common ordnance types. Therefore, the results presented above may only be confidently applied to the 3lb bomb. 41 Chapter 5: Numeric Simulations: Temporal Variations 5.1 Introduction When analysing a dataset, there is limited information provided about the depth or orientation of any given UXO. As such, the simulations performed in Chapters 3 and 4, while important to developing an understanding of the factors influencing the shape and magnitude of a TEM response, provide insufficient information for developing a workflow to distinguish between two-peak anomalies due to one or two targets. In this chapter, I explore what information may be gleaned from the dataset as a function of time. In particular, I focus on how the peak separation, peak widths, maxima values and maxima to minimum ratios of the TEM response behave with time. 5.2 Synthetic Datasets Two synthetic datasets are considered in this chapter: a) a single object dataset and, b) a two-object dataset. The two datasets are normalized to their respective maxima values at time channel 1 so that they are essentially indistinguishable from one another. In both cases, d and h are kept constant at 0.2 m and 0.3 m, respectively. For the single object dataset, a 3lb bomb is oriented such that ! " = 90°. For the two-object dataset two 3lb bombs are placed 0.8 m apart with ! " = 0°. The sample spacing in both cases is 0.25 m. Both datasets are shown in Figure 5.1 for time channel 1. As seen in Figure 5.1, the two-target scenario produces a TEM response similar to the single body problem. The absolute and relative differences between the datasets are calculated. The absolute difference is calculated by ! V D s "V S s , where ! V D s and ! V S s are the voltages induced at the receiver due to the secondary response of the two and one- 42 target cases, respectively. The relative difference is calculated: ! V D s "V S s V D s . The absolute difference between the two datasets is very small, on the order of ! 10 "3 mV , and the relative difference is up to 20%. These differences are very small and it is clearly difficult to distinguish between the one and two object cases. However, inverting both datasets for a single object using UXOLab, only the one-object dataset is fit successfully. The inversion results are briefly discussed in Appendix B. The two datasets are fundamentally different, but difficult to distinguish qualitatively. Figure 5.1 – Synthetic datasets at time channel 1: a two-peak anomaly produced by a single UXO (top left) and a two-peak anomaly produced by two UXO (top right). Both datasets are normalized to their respective maxima values. The absolute (bottom left) and relative (bottom right) differences are also shown. 43 5.3 Comparison of Synthetic Datasets Figures 5.2 and 5.3 show the peak separations ( ! w 1 ), peak widths ( ! w 2 ), maxima to minimum ratios ( ! m i s ), and maxima values ( ! m 1 ,m 2 ) values through time for the one and two-target datasets, respectively. Figure 5.2 – Peak separation, peak width, maxima values and maxima to minimum ratios through time for the single target dataset. 44 Figure 5.3 – Peak separation, peak width, maxima values and maxima to minimum ratios through time for the two target dataset. At first glance, Figures 5.2 and 5.3 look very similar. The shapes of the curves for each characteristic behave almost identically, but the dynamic ranges of some of the curves are different. For both scenarios, ! w 1 remains constant through time at ! w 1 =1.0 m . The dynamic range of ! w 2 for the single target scenario is approximately 4 times that of the two-target scenario. The dynamic range of ! m i s also differs – in the single target case it is approximately 20 times greater than that of the two-target case. The magnitudes of the maxima values through time behave identically for both cases. These values decay exponentially and the manner in which they decay may be of interest. From this brief comparison, three possibly distinguishing features become apparent: differences in the behaviours of peak width, maxima to minimum ratios and maxima value decays may be used as diagnostic features of any TEM signal. 45 5.4 Further Modeling of Temporal Variations To observe the behaviours of peak width, maxima to minimum ratios and maxima value decays further, another forward model is performed: the two-target case is modeled for changes in ! " . In these forward models, one target (target 1) is held spatially fixed at ! x = "0.4 m, with ! " = 0°, while the other (target 2) is allowed to rotate about its centre from ! 0° to ! 90° at ! 10° intervals. The sample interval of the dataset is 0.10 m. ! w 2 , m i s and ! m i are recorded through time. For both the peak widths and maxima to minimum ratios, the desire is to determine if the dynamic range of these values remains fixed for all ! " . If this is the case, these variables may be criteria for distinguishing between multi-peak anomalies produced by one or two-targets. The decays of the maxima values are fit to determine if any information can be gained from their decay parameters. 5.4.1 Peak Width Figure 5.4 is a plot of ! w 2 for both peaks of the two-body case. The solid and dashed lines show the peak widths of peak 1 ( ! w 2,1 ) and peak 2 ( ! w 2,2 ), respectively. Only ! 40° "# " 70° is considered to observe the behaviour of ! w 2 through mid- ! " . This is done primarily because of programming problems involving the determination of the peak widths. These problems introduce large discontinuities in some ! w 2 curves, which is believed to be due to the sampling interval of the dataset. The curves shown in Figure 5.4 are believed to be valid as they contain no discontinuities. This assumption may be inappropriate; the conclusions made from these simulations may not necessarily be accurate. The goal of the simulation performed in this section is merely to observe the dynamic range of ! w 2,1 and ! w 2,2 through time, for different ! " . 46 Figure 5.4 – Peak width for the two-target scenario for varying ! " through time. The solid lines are the peak widths of peak 1 and the dashed lines are the peak widths of peak 2. ! w 2,1 behaves consistently: for all ! " , ! w 2,1 is approximately constant. However, an increase in the dynamic range of ! w 2,2 with increasing ! " is observed. Following from Figure 4.5, it is expected at all ! w 2,1 should be approximately equal for the first time channel. If this is the case, all ! w 2,1 curves should begin at the same point. This is not observed. 5.4.2 Maxima to Minimum Ratios Figures 5.5a and 5.5b show the maxima to minimum ratios of both peaks for the two-target case. The dynamic range of the maxima to minimum ratio calculated using the first peak ( ! m 1 , associated with target 1) increases as the ! " of the adjacent object (target 2) increases. The dynamic range of the maxima to minimum ratio calculated 47 using the second peak ( ! m 2 , associated with target 2) also generally increases with ! " , but as shown in Figure 5.5b, the ratio for ! " = 60° through time is larger that that for ! " = 90°. The magnitude of the ratios are significantly different for both peaks: ! m 1 s has a maximum value of ~47 when ! " = 90° and ! m 2 s has a maximum value of ~16 when ! " = 60°. Figure 5.5 – Maxima to minimum ratios for peak 1 (5.5a, left) and peak 2 (5.5b, right). 5.4.3 Maxima Decay The decays of the maxima of the two peaks for both scenarios are exponential and are fit to an equation of the form of ! m i (t) = k i t "# i e " t $ i (recall Equation 14). The ! " parameters for both ! m 1 and ! m 2 are found to be ~0.88 and the ! " gamma parameters, ~1.86. These approximate the axial dipole decay parameters of the 3lb bomb well ( ! " 1 = 0.87 and ! " 1 =1.85), and as Figure 5.6 shows, the maxima decay curves correspond 48 to the ! L 1 (t) curve of the 3lb bomb. Figure 5.6 is normalized to the maximum value of each curve so that the correlation between the decays of the curves may be plainly seen. By doing this, however, information about ! k , the amplitude of the curve, is lost. Figure 5.6 – The normalized decays of the maxima values through time for the single- target (left) and two-target (right) scenarios. Varying the depth of burial, d, and the angle of rotation of the targets, ! " , finds the same decay (see Figures 5.7 to 5.9). This implies that the shape of decay of the maxima values with time is independent of the orientation of the target. The magnitudes of the maxima values, however are dependent on the orientation of the target. 49 Figure 5.7 – The decays of the maxima values through time for the single-target scenario. The decays of ! m 1 (left) and ! m 2 (right) are observed for varying burial depths. Figure 5.8 – The decays of the maxima values through time for the single-target scenario. The decays of ! m 1 (left) and ! m 2 (right) are observed for varying ! " . 50 Figure 5.9 – The decays of the maxima values through time for the two-target scenario. The decays of ! m 1 (left) and ! m 2 (right) are observed for varying ! " . 5.5 Conclusion 5.5.1 Peak Separation In Section 5.2 two datasets were presented which produced very similar TEM responses. One was simulated using a single, horizontal 3lb bomb, while the other was simulated using two vertical 3lb bombs separated by a distance of 0.8 m. Peak separation was found to be identical through time for both simulations. This implies that the positions of the local maxima are invariant through time. Based on these observations, the behaviour of ! w 1 through time does not appear to be an indication of target number in the subsurface. 51 5.5.2 Peak Width Figure 5.4 shows the peak widths ( ! w 2 ) through time for both peaks of the two- target scenario. In this configuration, one target’s orientation is held fixed while the other’s is allowed to vary in ! " . The peak widths of the response of the fixed target (target 1) have the same dynamic range and shape, with the curve itself being translated up or down for different ! " . For the second peak, the peak generated by the target with varying ! " , the dynamic range of ! w 2 appears to increase with increasing ! " , therefore ! w 2 is not particularly useful as a diagnostic characteristic if the orientation of the target is not known. 5.5.3 Maxima to Minimum Ratios The inconsistencies noted in Figure 5.5b can be explained by considering the interaction of the TEM responses of the individual targets. Target 1 produces the anomaly centred on ! m 1 . This target remains fixed in space, such that ! " = 0°, therefore the effect of the TEM response of the target on the maxima to minimum ratio should remain constant throughout the entire simulation. Target 2, on the other hand, is allowed to rotate from ! 0° "# " 90°. Initially, when ! " = 0°, the maxima to minimum ratio of target 2 is the same as that of target 1. The saddle point, s, between the two maxima anomalies is determined by the spatial separation of the two targets in the subsurface. If target 1 and target 2 are closely spaced, the value of s will be relatively large. As the spatial separation of the targets increases, s will approach the value of the TEM response of the background host material. The ratio ! m i s is therefore dependent on the separation between targets, of which, in practice, we have no information. 52 In Figure 5.5b, the ! m i s curves cross because s is dependent on the strength of the TEM responses of the individual targets. The total TEM response is simply the linear combination of the two individual responses, therefore if the response due to target 2 is relatively small, the value of s will increase. Additionally, as target 2 rotates and produces two peaks, the peak closest to the peak generated by target 1 will become superimposed on the anomaly due to target 1. This will serve to increase the value of ! m 1 . This explains why the dynamic range of ! m 1 s increases as target 2 increases. Varying ! " , it is observed that the maxima to minimum ratio is very dependent on orientation. Only when ! " is very small for both targets is the dynamic range of ! m i s small. If we attempt to apply this procedure to two target scenarios in which one of the targets is oriented perpendicular to the ground surface and the other is at ! " # 0°, we encounter a situation in which we have bleed over of the signals, resulting in a maxima to minimum ratio which increases as ! " increases. This limits the usefulness of the maxima to minimum ratios to the end member problems of two vertical UXO versus one horizontal UXO. 5.5.4 Decay of the Maxima Values In Section 5.4.3, the decay of the maxima points of the EM signal is examined. While the amplitudes of the maxima points are dependent on orientation, the decay of the curves is not. This is a powerful tool, however, as shown in Figure 5.6, it cannot be used to identify a multi-peak anomaly produced by two targets of the same type. Since the decay of the maxima values is defined by the characteristic properties of the UXO, two 53 items of the same type will decay in the same manner. Further, as seen in Figures 5.7 and 5.8 , the amplitude of the maximum value is dependent on depth and θ. As such, two decay curves with the same decay parameters but of different magnitudes may be indicative of two objects of the same type buried at depth or one object oriented such that θ is less than 90° but larger than 30°. This tool is most applicable to identifying two targets of different types from multi-peak anomalies as the decays of the two curves will be different due to the material and physical properties of the target. 54 Chapter 6: Synthetic Example: Two Targets of Different Types 6.1 Introduction In Section 5.4.3 I examined the decay of the maxima values through time for two possible scenarios: a one-target case and a two-target case. I found that the maxima values in both scenarios decayed according to the unique polarizations of the target. In this chapter, I expand this idea to a two-target scenario in which the UXO targets are of different types. 6.2 Synthetic Dataset A synthetic dataset is created by modelling a 3lb bomb at x = 0.4 m with ! " =10° and an ATC 105 mm at x = -0.4 m with ! " = 70°. The plan view and profile along y = 0.0 m for this dataset at time channel 1 are shown in Figure 6.1. A clear two-peak anomaly is observed. The dataset is inverted for a single body using UXOLab, and is unsuccessfully fit (see Appendix B). 55 Figure 6.1 – The test dataset: plan view (left) and line profile (right) taken across the anomaly peaks, for y = 0.0 m. 6.3 ! L(t) Curves for the 3lb Bomb and ATC 105 mm The polarization curves ( ! L(t)) for both the 3lb bomb and the ATC 105 mm are plotted in Figure 6.2. The polarization curves of the 3lb bomb decay more rapidly than those of the ATC 105 mm, therefore, it is expected that the TEM response due to the ATC 105 mm will dominate the signal at late time channels. In general, the response of the ATC 105 mm is expected to be larger than that of the 3lb bomb as the amplitudes of the polarization curves are always greater than that of the 3lb bomb. The TEM response, however, is dependent on depth, therefore this generalization does not necessarily hold. 56 Figure 6.2 – The ! L 1 (t) (red) and ! L 2 (t) (blue) curves for the 3lb bomb (dashed lines) and the ATC 105 mm (solid lines). 6.4 Maxima Decay Figure 6.3 shows the polarization curves and maxima decays plotted without normalization (Figure 6.3a) and plotted normalized to 1 (Figure 6.3b). In Figure 6.3a, the ! m 1 and ! m 2 curves cross at intermediate time. At early times, the magnitude of ! m 1 is greater than ! m 2 , but at later times, because ! m 1 decays so rapidly, ! m 2 is larger. Plotting the normalized maxima values of the dataset through time along with the normalized polarization curves, an interesting trend is noted: ! m 2 decays according to the ! L 1 (t) for the 3lb bomb at early time channels, then appears to veer toward the ! L 1 (t) of the ATC 105 mm at late times. The decay of ! m 1 lies between the polarization curves of the ATC 105 mm. 57 Figure 6.3 – The non-normalized (6.3a, left) and normalized (6.3b, right) polarization curves and decays of ! m 1 and ! m 2 for the test scenario. 6.5 Conclusion As observed in Section 6.4, the maxima decay curves for ! m 1 and ! m 2 actually intersect at intermediate times. Since the amplitude of the maxima values is dependent on depth, the amplitude of the maxima due to the ATC 105 mm ( ! m 1 ) is expected to be smaller than that of the 3lb bomb ( ! m 2 ) as it is more deeply buried. However, recalling Figure 6.2, it is noted that the polarization curves of the 3lb bomb decay much more rapidly than those of the ATC 105 mm. This suggests that the signal due to the 3lb bomb will die out more quickly than the signal due to the ATC 105 mm, therefore at later time channels the ATC 105 mm response is more dominant. ! m 2 veers from the ! L 1 (t) for the 3lb bomb to the ! L 1 (t) for the ATC 105 mm. Again, this has to do with the decay rates of the polarizations. In the case of the 3lb 58 bomb, ! L 1 (t) decays more rapidly then for the ATC 105 mm, therefore, at late time channels the signal due to the ATC 105 mm is dominant. In addition, the occurrence of the two-peaks due to the ATC 105 mm at late times will contaminate ! m 2 , thus explaining why at late times ! m 2 behaves according to the polarizations of the ATC 105 mm. ! m 1 does not lie directly on the ! L 1 (t) curve for the ATC 105 mm. This is because ! L 1 (t) is not as dominant for the ATC 105 mm as it is for the 3lb bomb. ! L 1 (t) is particularly large for the 3lb bomb, and therefore dominates any response produced by the ordnance. For most UXOs, however, the ratio between ! L 1 (t) and ! L 2 (t) is not very large. As such, the decays of the maxima values due to UXOs should, in general, fall between the ! L 1 (t) and ! L 2 (t) . By knowing the polarization curves of the UXOs possibly contaminating a particular site, and comparing the maxima values of any two-peak anomalies through time with the decay of these polarization curves, it is possible to discriminate between anomalies produced by one target or two targets with different characteristic properties. In this case, the decays of the maxima values through time will be different. If two curves with the same decay parameters are present, two possibilities exist: a) one target is oriented such that θ is less than 90° but greater than 30°; or b) two targets of the same type are buried at different depths with both their θ values less than 30°. In the first case, a single UXO is capable of producing two peaks of different magnitudes, while in the last, both objects produce single peak anomalies of different magnitudes. Finally, if both ! m 1 and ! m 2 through time plot on the same curve, two possibilities present themselves: a) the anomaly is produced by a single target, or b) the anomaly is produced by two targets of the same type and buried at the same depth. 59 Chapter 7: Conclusion The problem of UXO contamination is widespread and efficient discrimination techniques must be developed in order to minimize the cost of UXO remediation. Most of the cost associated with UXO remediation is spent one excavation of non-UXO targets (Berans 2005). Another significant problem is the occurrence of single UXOs which may produce multi-peak anomalies (Pasion 2007). These pose a great deal of difficulty to the process of anomaly discrimination as they are often mistaken for multiple targets. This paper sought to examine this problem more carefully in the hopes of developing a workflow for understanding multi-peak anomalies. 7.1 General Conclusions from Previous Chapters In Chapter 3, an analytic approximation was presented using the two-dipole approximation. This approximation models the response of an axi-symmetric UXO as the linear combination of two mutually orthogonal dipoles. The axial polarization, ! L 1 (t) , and transverse polarization, ! L 2 (t) , curves were introduced and the effect of the ratio between the two, ! L 1 (t) L 2 (t) , on the TEM response was modelled. From this model, it was determined that multi-peak anomalies occur when ! L 1 (t) L 2 (t) " 3. Therefore, if the arsenal of UXOs is known for an area in need of remediation, it is possible to predict if multi-peak anomalies due to a single target are possible by calculating ! L 1 (t) L 2 (t) for all expected UXOs. In Chapter 4, the effects of changing the depth and orientation of a UXO on the TEM response were examined. For these models, the 3lb bomb was used. This ordnance 60 is capable of producing a two-peak anomaly for all time channels. From these investigations, it was determined that not only must ! L 1 (t) L 2 (t) " 3, but ! " must be greater than or equal to ! 30° for a two-peak anomaly to be produced. Peak separation ( ! w 1 ) is approximately constant for all ! " . The peak width of the peak with the greatest magnitude remains relatively constant while the peak width of the second peak increases slightly as ! " increases. The TEM response is symmetrical for ! " = 90°. With increasing target depth, the magnitude of the TEM response decreases. The behaviour of peak separation, peak width, maxima to minimum ratio and maxima values with time are observed in Chapter 5. Peak separation is found to remain constant through time, while peak width and maxima to minimum ratios become subject to “bleed-over” contamination by adjacent targets. These three characteristics do not yield themselves as particularly useful indicators of multi-peak anomalies produced by one or two targets. The magnitudes of the maxima values of each peak are found to decay through time in accordance with the decays of the polarization curves of the UXO. This idea is further explored in Chapter 6, where the maxima values of a two-peak anomaly are plotted as a function of time. The anomaly is produced by two targets with different material and physical properties. The decays of the both maxima through time are different, but in accordance with the polarization curves of the targets which produce them. 61 7.2 A Workflow for Understanding Multi-peak Anomalies for UXO Discrimination Based on the conclusions outlined in Section 7.1 a workflow for understanding multi-peak anomalies for UXO discrimination may be outlined. This workflow is shown in Figure 7.1. 62 Figure 7.1 – Workflow for discriminating between multi-peak anomalies produced by one and two targets in the subsurface. 63 7.3 Assumptions and Limitations In the research presented in this thesis, certain assumptions are made to both define and simplify the two-peak anomaly problem: 1) It is assumed that the type of UXO being explored for is known. This assumption enables us to use the polarization curves of the UXO during the discrimination process (Chapter 6). 2) The depths, d, and orientations, ! " , of the UXO are unknown. 3) The analysis performed is restricted to two peak anomalies. The conclusions reached in this these are limited by several factors. Firstly, the analysis performed focuses mainly on the 3lb bomb, therefore all conclusions derived may need to be adjusted for different ordnances. As explained earlier, the 3lb bomb is unique in its ability to produce a two-peak anomaly for all time channels, assuming it is oriented appropriately. All datasets examined were of excellent quality – they did not incorporate any noise, and were sampled densely (in some cases, 5 cm spacing). Data derived from field surveys are always polluted by noise and are not necessarily densely sampled, meaning that the quality of the data may be insufficient to apply the workflow outlined in Figure 7.1. 7.4 Future Work Further research is needed to expand on the conclusions presented in this paper. Since most of the analysis was performed using the 3lb bomb, the workflow presented in Section 7.2 must be tested for other ordnance types. The contributions of noise to the 64 problem must also be considered, since noise is always associated with practical survey conditions. The information presented in this thesis was derived using synthetic datasets of good quality, therefore the validity of the conclusions made must be tested to determine if they may be applied to proper field datasets. The problem of multi-peak anomalies due to two ordnances of the same type must also be further explored. Because the material and physical properties of the two targets are identical in this scenario, the behaviour of the decay of the maxima points through time will also be identical. This makes it very difficult to discriminate between multi- peak anomalies produced by single targets and two-targets of the same type. 65 Appendix A: Polarization Constants The constants in Equation 14 for the different ordnance types mentioned in this paper are presented in Table 1. The subscript 1 denotes constants for the axial polarization and the subscript 2 denotes constants for the transverse polarization. All constants are taken from UXOLab. Table 1 – Parameterization Constants for the Polarization Curves of Three UXOs UXO type ! k 1 ! " 1 ! " 1 ! k 2 ! " 2 ! " 2 3lb FLBGR Bomb 15.88000 0.870000 1.850000 0.590000 1.410000 2.200000 ATC 105 mm 41.174212 0.699056 11.977106 19.993885 0.824055 3.766922 ATC MK118 2.201114 0.398891 0.999278 3.199694 0.408589 1.943397 66 Appendix B: Inversions of Synthetic Data The inversions mentioned in Sections 5.2 and 6.2 are shown in Figures B1 to B3. The inversions were performed in UXOLab, using default settings. Each dataset was inverted for a single object and the anomalies were masked using 1.5 m, circular masks. Of the three inversions, only the inversion shown in Figure B1 was successful. This is the inversion of the single target dataset presented in Section 5.2, produced by modelling only one 3lb bomb with ! " = 90° and d = 0.2 m. ! x,y,z,",#,k 1 ,$ 1 ,% 1 ,k 2 ,$ 2 and % 2 are accurately determined and therefore the fit is deemed successful. Note that in UXOLab, z = d. 67 Figure B1 – Inversion of a synthetic dataset (see Section 5.2) where one 3lb bomb is oriented such that ! " = 90° and d = 0.2 m. The inversion is successful. 68 Figure B2 is the inversion of the two-object dataset introduced in Section 5.2. The inversion is unsuccessful and models a single object at the surface of the Earth oriented ! " = 90°. Figure B2 – Inversion of a synthetic dataset where two 3lb bomb are oriented such that ! " = 0° and d = 0.2 m. The objects are placed 0.8 m apart. The inversion is unsuccessful. 69 Figure B3 is the inversion of the two-object dataset introduced in Section 6.2. The inversion is unsuccessful and models a single object at a depth of 0.31 m below the surface of the Earth and an oriented ! " = 88.6°. Figure B3 – Inversion of a synthetic dataset where a 3lb bomb at x = 0.4 m with ! " =10° and an ATC 105 mm at x = -0.4 m with ! " = 70° are modelled. The inversion is unsuccessful. 70 Bibliography Beran, L. Classification of unexploded ordnance. Masters thesis, University of British Columbia, 2005. Billings, S. Discrimination and classification of buried unexploded ordnance using magnetometry. IEEE Transactions Geoscience & Remote Sensing, 42:1241 – 1251, 2004. Geonics Limited, EM63, www.geonics.com/html/em63.html. (accessed March 22, 2008). Gubbins, D. 2004. Time Series Analysis and Inverse Theory for Geophysicists. Cambridge: Cambridge University Press. Griffiths, D.J. 1999. Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice Hall. Oldenburg, D. 2007. Applied Geophysics: Electromagnetic Methods. Lecture notes presented in EOSC 454, at the University of British Columbia, Vancouver, Canada. Pasion, L.R. Inversion of Time Domain Electromagnetic Data for the Detection of Unexploded Ordnance. PhD thesis, University of British Columbia, 2007. Pasion, L.R., Billings, S.D., and Oldenburg, D.W. Locating and characterizing unexploded ordnance using time domain electromagnetic induction. Technical report, U.S. Army Research and Development Center, Vicksburg, MS, 2001. ERDC/GSL TR-01-10.
Graduating Project
eng
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Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Undergraduate
University of British Columbia. EOSC 449
UXO
multi-peak anomalies
Time-domain electromagnetic
TEM
two dipole approximation
polarization
depth
orientation
Understanding Multi-Peak Anomalies for Unexploded Ordnance Discrimination
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